Log-PCA versus Geodesic PCA of histograms in the Wasserstein space
Language
en
Article de revue
This item was published in
SIAM Journal on Scientific Computing. 2018, vol. 40, n° 2, p. B429–B456
Society for Industrial and Applied Mathematics
English Abstract
This paper is concerned by the statistical analysis of data sets whose elements are random histograms. For the purpose of learning principal modes of variation from such data, we consider the issue of computing the PCA of ...Read more >
This paper is concerned by the statistical analysis of data sets whose elements are random histograms. For the purpose of learning principal modes of variation from such data, we consider the issue of computing the PCA of histograms with respect to the 2-Wasserstein distance between probability measures. To this end, we propose to compare the methods of log-PCA and geodesic PCA in the Wasserstein space as introduced by Bigot et al. (2015) and Seguy and Cuturi (2015). Geodesic PCA involves solving a non-convex optimization problem. To solve it approximately, we propose a novel forward-backward algorithm. This allows a detailed comparison between log-PCA and geodesic PCA of one-dimensional histograms, which we carry out using various data sets, and stress the benefits and drawbacks of each method. We extend these results for two-dimensional data and compare both methods in that setting.Read less <
English Keywords
Non-convex optimization
Wasserstein Space
Geodesic Principal Componant Analysis
ANR Project
Generalized Optimal Transport Models for Image processing - ANR-16-CE33-0010
Origin
Hal imported